Pith Number

pith:OPHQFCT2

pith:2016:OPHQFCT2CSZCV3BYG36SN5X4TJ

not attested not anchored not stored refs pending

The sandpile model on K_{m,n} and the rank of its configurations

Michele D'Adderio, Yvan Le Borgne

arxiv:1608.01521 v1 · 2016-08-04 · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OPHQFCT2CSZCV3BYG36SN5X4TJ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T01:09:52.242574Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

73cf028a7a14b22aec3836fd26f6fc9a5c1ba462780b08429d2e1628b1547b0b

Aliases

arxiv: 1608.01521 · arxiv_version: 1608.01521v1 · doi: 10.48550/arxiv.1608.01521 · pith_short_12: OPHQFCT2CSZC · pith_short_16: OPHQFCT2CSZCV3BY · pith_short_8: OPHQFCT2

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/OPHQFCT2CSZCV3BYG36SN5X4TJ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 73cf028a7a14b22aec3836fd26f6fc9a5c1ba462780b08429d2e1628b1547b0b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "498f9b7e1d97ff809f64ecc41329fcba53863c5eac4d55e81f5b1c32e6687522",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-08-04T12:56:23Z",
    "title_canon_sha256": "58475645446fa3ffe0fe510a0d61c42583c6d41c1da2aafd4fc0c3fd08c80e40"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.01521",
    "kind": "arxiv",
    "version": 1
  }
}